After doing some testing, I found that if I specified the core framework (dnxcore50) to the build command, then it would work properly.

dnu build --framework dnxcore50

After doing some more digging, I found that I did not have the mono framework installed on the machine, and thus the v4.5.1 build was failing. To correct this, I simply had to install the mono framework using dnvm:

dnvm upgrade -r mono

After that, the dnu build works properly and I can continue on my way.